A way to solve math problems in chemistry Used to convert km to miles, m to km, mol to g, g to mol,...

• A way to solve math problems in chemistry• Used to convert

km to miles, m to km, mol to g, g to mol, etc.• To use this we need: 1) desired quantity,

2) given quantity, 3) conversion factors• Conversion factors are valid relationships or

equities expressed as a fractionE.g. for 1 km=0.6 miles the conversion factor is

The factor label methodThe factor label method

km 1

miles 0.6 or

miles 0.6

km 1

Q. write conversion factors for 1 foot =12 inchesQ. what conversion factors can you think of that

involve meters?

Conversion factorsConversion factorsConversion factors for 1 ft = 12 in

foot 1

inches 12 or

inches 12

foot 1

There are almost an infinite number of conversion factors that include meters:

mm 1000

m 1 ,

cm 100

m 1 ,

km 1

m 1000

m 1

yards 0.9144 ,

inches 39.37

m 1 ,

feet 3.28

m 1

Conversion factorsConversion factors• We have looked at conversion factors that are

always true. There are conversion factors that are only true for specific questions

• E.g. A recipe calls for 2 eggs, 1 cup of flour and 0.5 cups of sugar

• We can use these conversion factors

sugar cups 0.5

eggs 2 ,

flour cup 1

sugar cups 0.5 ,

flour cup 1

eggs 2

The steps to followThe steps to followNow we are ready to solve problems using the

factor label method. The steps involved are:

1. Write down the desired quantity/units

2. Equate the desired quantity to given quantity

3. Determine what conversion factors you can use (both universal and question specific)

4. Multiply given quantity by the appropriate conversion factors to eliminate units you don’t want and leave units you do want

5. Complete the math

Factor label exampleFactor label exampleQ - How many kilometers are in 47 miles?

(note: 1 km = 0.621 miles)

First write down the desired quantity

# km

Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles)

Next, equate desired quantity to the given quantity

# km = 47 mi

Factor label exampleFactor label example


Now we have to choose a

conversion factor

# km = 47 mi



What conversion factors are possible?

# km = 47 mi 1 km 0.621 mi

0.621 mi 1 km



Pick the one that will allow you to cancel

out miles

# km = 47 mi 1 km 0.621 mi

0.621 mi 1 km


Pick the one that will allow you to cancel

out miles


# km = 47 mi 1 km 0.621 mi

0.621 mi 1 km



Multiply given quantity by chosen conversion factor

# km = 47 mi 1 km 0.621 mi

0.621 mi 1 km



Multiply given quantity by chosen conversion factor

# km = 47 mi x 1 km 0.621 mi



Cross out common factors

# km = 47 mi x 1 km 0.621 mi



Cross out common factors

# km = 47 x 1 km 0.621



Are the units now correct?

# km = 47 x 1 km 0.621



Yes. Both sides have km as units.

# km = 47 x 1 km 0.621



Yes. Both sides have km as units.

# km

= 47 x 1 km 0.621

# km



Now finish the math.

# km = 47 x 1 km 0.621

= 75.7 km



The final answer is 75.7 km

# km = 47 x 1 km 0.621

= 75.7 km


SummarySummary

The previous problem was not that hard

In other words, you probably could have done it faster using a different method

However, for harder problems the factor label method is easiest

More examplesMore examples1. You want to buy 100 U.S. dollars. If the

exchange rate is 1 Can$ = 0.65 US$, how much will it cost?

# Can$ = 100 US$ x 1 Can$ 0.65 US$

= 153.85 Can$

More examplesMore examples2. There are 12 inches in a foot, 0.394 inches

in a centimeter, and 3 feet in a yard. How many cm are in one yard?

# cm = 1 yd x 3 ft 1 yd

= 91.37 cmx 12 in

1 ft x 1 cm

0.394 in

The Chemist's Dozen: Avogadro’s Number

• Chemists count atoms, molecules and ions in groups called moles. (abbreviated mol).

• The number 6.02 x 1023

is called Avogadro’s number (NA)

• 1 mol = 6.02 x 1023

What 2 factors can you make from that relationship?

1mol and 6.02 x 1023

6.02 x 1023 1 mol

The unit with Avogadro’s number could be atoms, ions or molecules.

Let’s do a calculation

A sample contains 1.25 mol of nitrogen dioxide molecules.

a. How many molecules are in the sample?

b. How many atoms are in the sample?

a. How many molecules?

• x molecules NO2 = 1.25 mol x conversion

factor

Which factor is appropriate?

1mol or 6.02 x 1023 molecules

6.02 x 1023 molecules 1 mol

How many molecules in 1.25 moles?• x molecules = 1.25 mol x 6.02 x 1023 molecules

1 mol

= 7.525 x 1023 molecules

The unit mol cancels out and we have the unit molecules in our answer.

How many atoms in 1.25 moles of NO2?

• There are 2 relationships we need.

• 1 mol = 6.02 x 1023 molecules

• 1 molecule of NO2 contains 3 atoms of

• 1 molecule = 3 atoms.

• Note this last factor is specific to NO2. It would not be the same for CH4 or other molecules.

How many atoms in 1.25 moles NO2?

x atoms in NO2 = 1.25 mol NO2 x 6.02 x 1023 molecules NO2 x 3 atoms in NO2 1 mol NO2 1 molecule NO2

Use the units to guide the calculation. NO2 is a compound so its particles are molecules. We used that in part a. In part b we want to know how many atoms are in the 1.25 mol sample so we add a conversion factor that shows that there are 3 atoms (1 N and 2 O) atoms in each molecule of NO2.

After doing the math

x atoms in NO2 = 1.25 x 6.02 x 1023 x 3 atoms = 2.58 x 1023 atoms

This could also be done as a 2 step problem using your answer from part a followed by the 3 atom/1 molecules conversion factor.

A way to solve math problems in chemistry Used to convert km to miles, m to km, mol to g, g to mol,...

Documents

Transcript of A way to solve math problems in chemistry Used to convert km to miles, m to km, mol to g, g to mol,...